Problem: Multiply the following complex numbers: $({-4-i}) \cdot ({0})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-4-i}) \cdot ({0}) = $ $ ({-4} \cdot {0}) + ({-4} \cdot {0}i) + ({-1}i \cdot {0}) + ({-1}i \cdot {0}i) $ Then simplify the terms: $ (0) + (0i) + (0i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (0 + 0)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (0 + 0)i - 0 $ The result is simplified: $ (0 - 0) + (0i) = 0 $